We start with a simple problem in geometry in the spirit of the ones discussed in Chapter 1. Given two lines in 2D, find their point of intersection (see Figure 3.1). Suppose the equations of the lines are
l1 : a1x+ b1y + c1 = 0 ,
l2 : a2x+ b2y + c2 = 0 . (3.1)
l1 : a1x+ b1y + c1 = 0
l2 : a2x+ b2y + c2 = 0
Stating that problem slightly differently, we are looking for a point (x, y) that lies on both lines, i.e., satisfies Equations (3.1).